{"id":1564,"date":"2023-05-25T16:52:56","date_gmt":"2023-05-25T11:22:56","guid":{"rendered":"https:\/\/escortsservice.com.au\/blog\/you-can-probably-beat-chatgpt-at-these-math-brainteasers-heres-why\/"},"modified":"2023-05-25T16:52:56","modified_gmt":"2023-05-25T11:22:56","slug":"you-can-probably-beat-chatgpt-at-these-math-brainteasers-heres-why","status":"publish","type":"post","link":"https:\/\/escortsservice.com.au\/blog\/you-can-probably-beat-chatgpt-at-these-math-brainteasers-heres-why\/","title":{"rendered":"You Can Probably Beat ChatGPT at These Math Brainteasers. Here&#8217;s Why"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div>\n<p>It turns out that if you want to solve a brainteaser, it helps to have a brain.<\/p>\n<p>ChatGPT and other artificial intelligence systems are earning accolades for feats that include <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/ai-chatbots-can-diagnose-medical-conditions-at-home-how-good-are-they\/\">diagnosing medical conditions<\/a>, <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/i-gave-chatgpt-an-iq-test-heres-what-i-discovered\/\">acing an IQ test<\/a> and <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/research-summaries-written-by-ai-fool-scientists\/\">summarizing scientific papers<\/a>. But <em>Scientific American<\/em> wanted to see what would happen if the bot went head to head with the legacy of legendary puzzle maker <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/blogs.scientificamerican.com\/guest-blog\/the-top-10-martin-gardner-scientific-american-articles\/\">Martin Gardner<\/a>, longtime author of our Mathematical Games column, who passed away in 2010. I tested ChatGPT on a handful of text-based brainteasers described by Gardner or a <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/math-games-of-martin-gardner-still-spur-innovation\/\">2014 tribute to his work<\/a> by mathematician Colm Mulcahy and computer scientist Dana Richards in <em>Scientific American<\/em>.<\/p>\n<p>The results ranged from satisfactory to downright embarrassing\u2014but in a way that offers valuable insight into how ChatGPT and similar artificial intelligence systems work.<\/p>\n<p>ChatGPT, which was created by the company OpenAI, is built on what\u2019s called a large language model. This is a deep-learning system that has been fed a huge amount of text\u2014whatever books, websites and other material the AI\u2019s creators can get their hands on. Then humans train the system, teaching it what types of responses are best to various kinds of questions users might ask\u2014particularly regarding sensitive topics.<\/p>\n<p>And that\u2019s about it.<\/p>\n<p>The AI \u201cdoes not have reasoning capabilities; it does not understand context; it doesn\u2019t have anything that is independent of what is already built into its system,\u201d says Merve Hickok, a policy researcher at the University of Michigan, who focuses on AI. \u201cIt might sound like it is reasoning; however, it is bound by its data set.\u201d<\/p>\n<p>Here\u2019s how some relatively simple puzzles can illustrate this crucial difference between the ways silicon and gray matter process information.<\/p>\n<h2>Puzzle 1<\/h2>\n<p>First, let\u2019s explore a true logic problem. As described in the 2014 tribute, \u201c<a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/martin-gardner-fans-try-these-mathematical-games\/\">There are three on\/off switches on the ground floor of a building<\/a>. Only one operates a single lightbulb on the third floor. The other two switches are not connected to anything. Put the switches in any on\/off order you like. Then go to the third floor to check the bulb. Without leaving the third floor, can you figure out which switch is genuine? You get only one try.\u201d<\/p>\n<p>When I fed this into the AI, it immediately suggested turning the first switch on for a while, then turning it off, turning the second switch on and going upstairs. If the lightbulb is on, the second switch works. If the lightbulb is off but warm, the first switch works. If the lightbulb is off and cold, the third switch works. That\u2019s exactly <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/answers-to-puzzles-posed-in-let-the-games-continue\">the same reasoning we suggested in 2014<\/a>.<\/p>\n<p>But ChatGPT\u2019s easy victory in this case may just mean it already knew the answer\u2014not necessarily that it knew how to determine that answer on its own, according to Kentaro Toyama, a computer scientist at the University of Michigan.<\/p>\n<p>\u201cWhen it fails, it looks like it\u2019s a spectacularly weird failure. But I actually think that all the instances in which it gets logic right\u2014it\u2019s just proof that there was a lot of that logic out there in the training data,\u201d Toyama says.<\/p>\n<h2>Puzzle 2<\/h2>\n<p>How about something with more math? In Gardner\u2019s words from his <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/issue\/sa\/1958\/08-01\/\">August 1958<\/a> column, \u201cTwo missiles speed directly toward each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start 1,317 miles apart. Without using pencil and paper, <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/blogs.scientificamerican.com\/guest-blog\/the-top-10-martin-gardner-scientific-american-articles\/\">calculate how far apart they are<\/a> one minute before they collide.\u201d<\/p>\n<p>ChatGPT made a solid effort on this one. It demonstrated two different approaches to a key piece of the puzzle: calculating the total distance the two missiles travel in one minute. In both cases, it found the correct answer of 500 miles, which is also the final answer to the puzzle. But the AI couldn\u2019t let go of the fact that the missiles began 1,317 miles away, and it kept trying to subtract the 500 miles from that distance, offering the incorrect answer that the missiles would be 817 miles apart one minute before the crash.<\/p>\n<p>I tried following up in a way that would encourage ChatGPT to find the correct answer. For instance, I suggested it respond to the question the way a professor of mathematics would and plainly said its answer was incorrect. These interventions failed to dissuade ChatGPT from offering the wrong solution. But when told the starting distance between the missiles was a red herring, it did adjust its response accordingly and find the correct answer.<\/p>\n<p>Still, I was suspicious about whether the AI had actually learned. I gave it the same puzzle but turned the missiles into boats and changed the numbers\u2014and alas, ChatGPT was once again fooled. That\u2019s evidence for what Toyama says is a big controversy in the field of AI right now: whether these systems will be able to figure out logic on their own.<\/p>\n<p>\u201cOne thesis is that if you give it so many examples of logical thinking, eventually the neural network will itself learn what logical thinking looks like and then be able to apply it in the right instances,\u201d Toyama says. \u201cThere are some [other] people who think, \u2018No, logic is fundamentally different than the way that neural networks are currently learning, and so you need to build it in specifically.\u2019\u201d<\/p>\n<h2>Puzzle 3<\/h2>\n<p>The third puzzle I tried came from a <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/issue\/sa\/1964\/03-01\/\">March 1964<\/a> Gardner column on prime numbers: \u201cUsing each of the nine digits once, and only once, form a set of three primes that have the lowest possible sum. For example, the set 941, 827 and 653 sum to 2,421, but this is far from minimal.\u201d<\/p>\n<p>A prime is a number that cannot be evenly divided by any number besides 1 and itself. It\u2019s relatively easy to assess small primes, such as 3, 5, 7 and 11. But the larger a number gets, the more difficult it becomes to evaluate whether that number is prime or composite.<\/p>\n<p>Gardner offered a particularly elegant solution the <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/issue\/sa\/1964\/04-01\/\">following month<\/a>: \u201cHow can the nine digits be arranged to make three primes with the lowest possible sum? We first try numbers of three digits each. The end digits must be 1, 3, 7 or 9 (this is true of all primes greater than 5). We choose the last three, freeing 1 for a first digit. The lowest possible first digits of each number are 1, 2 and 4, which leaves 5, 6 and 8 for the middle digits. Among the 11 three-digit primes that fit these specifications it is not possible to find three that do not duplicate a digit. We turn next to first digits of 1, 2 and 5. This yields the unique answer 149 + 263 + 587 = 999.\u201d<\/p>\n<p>I was genuinely impressed by the AI\u2019s first answer: 257, 683 and 941\u2014all primes, representing all nine digits and summing to 1,881. This is a respectably low total, even though it\u2019s higher than Gardner\u2019s solution. But unfortunately, when I asked ChatGPT to explain its work, it offered a verbose path to a different solution: the numbers 109, 1,031 and 683\u2014all primes but otherwise a poor fit for the prompt\u2019s other requirements.<\/p>\n<p>Upon being reminded of its initial answer, ChatGPT offered a daft explanation, including a claim that \u201cwe cannot use 1, 4, or 6 as the first digit of a three-digit prime, as the resulting numbers would be divisible by 3.\u201d This is patently false: you can recognize numbers divisible by 3 because their digits total a number divisible by 3.<\/p>\n<p>I attempted a pep talk, noting that there was a better solution and suggesting ChatGPT imagine it was a math professor, but it next offered 2, 3 and 749. It then stumbled to 359, 467 and 821\u2014another valid trio of primes, totaling 1,647\u2014better than its first solution but still not as elegant as Gardner\u2019s.<\/p>\n<p>Alas, it was the best I would get. Six more answers were riddled with nonprime numbers and missing or excess digits. And then ChatGPT once again offered 257, 683 and 941.<\/p>\n<p>All these failures reflect what Toyama says is a key property of these sorts of AI systems. \u201cChatGPT excels at the humanlike,\u201d he says. \u201cIt\u2019s mastered the style of being linguistically human, but it doesn\u2019t have explicit programming to do exactly the things that computers have so far been very good at, which is very recipelike, deductive logic.\u201d It isn\u2019t solving the problem, or necessarily even trying to\u2014it\u2019s just showing approximately what a solution might look like.<\/p>\n<p>Throughout the attempts, I was also struck that nothing seemed to fluster the AI. But Toyama says that\u2019s also a reflection of ChatGPT\u2019s creation and the material it was fed. \u201cThe vast majority of the data it was trained on, you could imagine the average tone of all of that text\u2014probably that <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scientificamerican.com\/article\/the-dunning-kruger-effect-isnt-what-you-think-it-is\/\">average tone is quite confident<\/a>,\u201d he says.<\/p>\n<h2>Puzzle 4<\/h2>\n<p>A final volley from the 2014 tribute: \u201cEach letter corresponds to a single digit&#8230;. Can you figure out which digit each letter represents to make the sum &#8230; work?\u201d<\/p>\n<figure class=\"image-captioned\"><img loading=\"lazy\" decoding=\"async\" alt=\"A substitution puzzle in which letters stand in for digits that are meant to be added together. Each of the first seven lines reads S E V E N; the last instance comes after a plus sign. Below the line signaling what to add is the word F O R T Y 9.\" height=\"759\" src=\"https:\/\/static.scientificamerican.com\/sciam\/assets\/Image\/2023\/puzzle4.png\" width=\"1230\"\/>&#13;<figcaption\/>&#13;<br \/>\n<\/figure>\n<p>This seemed elegant and fun! How bad could it be? Alas, ChatGPT\u2019s first response was \u201c11111 + 11111 + 11111 + 11111 + 11111 + 11111 + 11111 = F O R T Y 9.\u201d<\/p>\n<p>The AI\u2019s next offer acknowledged the substitution premise of the puzzle, but it took several rounds to convince the chatbot not to drop the second E in each S E V E N. ChatGPT seemed to stumble by chance on a combination including N = 7\u2014which was correct, miraculously, and the first step in the published solution.<\/p>\n<p>I confirmed N was accurate and then confronted the AI for apparently guessing at random. (If it was going to try out specific numbers, it should have started by testing different solutions for E. The easiest way to begin\u2014spoiler alert\u2014is by testing out E = 0, which ChatGPT completely failed to consider.) It promised a systematic solution, then guessed randomly again by positing that S = 1. While I\u2019d like to share the rest of that attempt, it was so nonsensical that it ended with \u201cUpdating the equation once more: 116,\u201d truly an illusion of an answer.<\/p>\n<p>ChatGPT got worse from there. Next, it assumed that S = 9, a choice I challenged it on. It posited that because N + N + N + N + N + N + N = 9, N = 1. It said that with seven E\u2019s whose sum must equal 2, E = 2. It even offered S =\u00a0<sup>4<\/sup>\u2044<sub>7<\/sub>, although it had the decency to shoot itself down over that one. I was losing hope in its ability to solve the puzzle, so I decided to help out more actively. I offered ChatGPT a clue: S = 3. When that was a nonstarter, I reminded the bot of N = 7 as well, but this merely yielded four increasingly gibberish answers.<\/p>\n<p>Once again, that gibberish is telling because it demonstrates how the AI handles any collection of facts it receives. In this sort of situation, although it appears the chatbot has forgotten that I said N = 7, Toyama says it is actually struggling with logic. \u201cThe responses it gives you after that all sound reasonable,\u201d he says, \u201cbut they may or may not be taking into account the right combination of facts or putting them together in the right way.\u201d<\/p>\n<p>In fact, you don\u2019t need to get nearly as sophisticated as these puzzles to see the ways ChatGPT struggles with logic, Toyama says. Just ask it to multiply two large numbers. \u201cThis is arguably one of the simplest kinds of questions of logic that you could ask; it\u2019s a straightforward arithmetic question,\u201d he says. \u201cAnd not only does it get it wrong once, it gets it wrong multiple times, and it gets it wrong in multiple ways.\u201d That\u2019s because even though ChatGPT has likely analyzed plenty of math textbooks, no one has given it an infinitely large multiplication table.<\/p>\n<p>Despite its struggles, the AI chatbot made one key logical breakthrough during the brainteasers. \u201cIt seems I\u2019m unable to accurately solve the given brainteaser at the moment,\u201d ChatGPT told me when I said it seemed to have run out of steam trying to crack the code of the last problem. \u201cI apologize for any frustration caused. It\u2019s best to approach the problem with a fresh perspective or consult other resources to find the correct solution.\u201d<\/p>\n<\/div>\n<p>[ad_2]<br \/>\n<br \/><a href=\"https:\/\/www.scientificamerican.com\/article\/you-can-probably-beat-chatgpt-at-these-math-brainteasers-heres-why\/\">Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] It turns out that if you want to solve a brainteaser, it helps to&hellip;<\/p>\n","protected":false},"author":1,"featured_media":1565,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[132],"tags":[],"class_list":["post-1564","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sexting"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>You Can Probably Beat ChatGPT at These Math Brainteasers. 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